Question

Imaginary Numbers and Conjugates: If z=2-3i and w=1+2i, evaluate z+w (conjugates of z, and w, and of z+w)

Answer 1

If \[z=2-3i\] and \[w=1+2i\] evaluate

Answer 2

The conjugate of the sums of the conjugates?

Answer 3

I believe, but I do not know for sure?

Answer 4

\[\begin{split}
\overline{\overline{a+bi}+\overline{c+di}} &= \overline{a-bi+c-di} \\
&=\overline{a+c-(b+d)i}\\
&=(a+c)+(b+d)i
\end{split}\]

Answer 5

The conjugate of the sum of the conjugates seems to just be the plain old sum.

Answer 6

I am going to try it right now, has to be better than what I had come up with.

Answer 7

\[
z=2−3i \implies \overline z = 2+3i
\]

Answer 8

\[
w=1+2i\implies \overline w=1-2i
\]

Answer 9

\[
\overline z+\overline w=(2+3i)+(1−2i)=3+i
\]

Answer 10

\[
\overline{\overline z+\overline w}=\overline{3+i}=3-i
\]

Answer 11

\[
z+w=(2−3i)+(1+2i)=3-i
\]

Answer 12

Seems consistent.

Answer 13

Awesome, so seems as though I got half of the answers right, the way I worked it out, I ended up with 4 answers. Mistook what I was looking at. Thank you so much!